SOLUTION: how would you find the partial decomposition of {{{ (10x+2)/((x+2)(x-4)) }}} would you factor the denominator and is it linear A/ax+b?

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: how would you find the partial decomposition of {{{ (10x+2)/((x+2)(x-4)) }}} would you factor the denominator and is it linear A/ax+b?      Log On


   

Question 1079454: how would you find the partial decomposition of +%2810x%2B2%29%2F%28%28x%2B2%29%28x-4%29%29+
would you factor the denominator and is it linear A/ax+b?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
A/(x+2) + B/(x-4)=10x+2/(x+2)(x-4)
multiply through by (x+2)(x-4)
A(x-4)+B(x-2)=10x+2
Ax-4A+Bx-2B=10x+2
x(A+B)=10x
-4A-2B=2, or 4A-2B=-2
A+B=10, so B=10-A
4A-20+2A=-2
6A=18
A=3
B=7
It is 3/(x+2) + 7/(x-4)